As observed by Baldwin and Shelah in [1]},
the expressive power of first-order logic in the colored structures
\({C} [\Sigma ^+]\)  is so strong that in the definitions of monadic stability and
monadic NIP it suffices to only consider formulas \(\varphi (x,y)\)  with
single free variables instead of tuples \(\bar{x},\bar{y}\) .
